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Strong approximations for partial sums of i.i.d.B-valued r.v.'s in the domain of attraction of a Gaussian law
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  • Published: March 1988

Strong approximations for partial sums of i.i.d.B-valued r.v.'s in the domain of attraction of a Gaussian law

  • Uwe Einmahl1 

Probability Theory and Related Fields volume 77, pages 65–85 (1988)Cite this article

Summary

We obtain a strong approximation theorem for partial sums of i.i.d.d-dimensional r.v.'s with possibly infinite second moments. Using this result, we can extend Philipp's strong invariance principle for partial sums of i.i.d.B-valued r.v.'s satisfying the central limit theorem toB-valued r.v.'s which are only in the domain of attraction of a Gaussian law. This new strong invariance principle implies a compact as well as a functional law of the iterated logarithm which improve some recent results of Kuelbs (1985).

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-5000, Köln 41, Federal Republic of Germany

    Uwe Einmahl

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  1. Uwe Einmahl
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Einmahl, U. Strong approximations for partial sums of i.i.d.B-valued r.v.'s in the domain of attraction of a Gaussian law. Probab. Th. Rel. Fields 77, 65–85 (1988). https://doi.org/10.1007/BF01848131

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  • Received: 21 January 1986

  • Revised: 01 October 1987

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF01848131

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Keywords

  • Stochastic Process
  • Probability Theory
  • Recent Result
  • Mathematical Biology
  • Central Limit
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